13 questions linked to/from Difficulties with bra-ket notation
3k views

• 1,064
Let $T$ be a linear operator, then we can consider the rank-one operator $$\vert Tx \rangle \langle y \vert.$$ I am wondering what is its adjoint operator, is it $$\vert y \rangle \langle T^*x \... • 117 0 votes 2 answers 921 views ### How to prove this identity for the complex conjugate of linear operator? I want to prove the following identity:$$\langle v|\Omega^{\dagger}|u\rangle = \langle u|\Omega | v \rangle^*$$How should I go about this? I believe I can prove it when \Omega is hermitian, but ... 0 votes 2 answers 207 views ### Associative product of two Anti-Linear(/Unitary) Operator An operator is said to be linear if it obeys the distributive law and commutes with the constant i.e. \hat{A}(a_1 |\psi_1\rangle + a_2|\psi_2\rangle)=a_1\hat{A}|\psi_1\rangle +a_2\hat{A}|\psi_2\... -1 votes 1 answer 279 views ### Property of the adjoint operator in the array element In Quantum Mechanics how can I prove this property?$$<\psi|A^{\dagger} |\phi>=<\phi|A|\psi>^{*}$$2 votes 1 answer 200 views ### Notation doubt - inner product I have a notational problem, I know when you define bra and ket you are defining an inner product, but you can see it as an linear operation where the linear operators (bras) act on vectors (kets), ... • 193 1 vote 2 answers 107 views ### Distributing operators inside of the bra and kets confusion I'm reading Griffiths and he has this section where he states that |\hat{Q}f\rangle is mathematical nonsense and that really we should write \hat{Q}|f\rangle, where the latter makes more sense to ... • 111 0 votes 2 answers 119 views ### Dirac expression derivation In Quantum Mechanics, 2nd Edition by Davies & Betts on page 78 it states that there is a symmetry implied by the following Hermitian operator equation:$${\displaystyle \int \phi^{*}(A \psi)d \,\...
I am confused as to what hermiticity of an operator means when given a basis set. My course notes say that hermitian operators in Hilbert space stay unchanged under it's complex conjugate: <n|A|m&...